in a Doppler-broadened Three-level System Using Spectral Decomposition Followed by Integration

In this study, we use spectral decomposition followed by integration to investigate a Doppler-broadened three-level Lambda type atomic system. On the basis of the transitions from the ground state to the decaying dressed states at various atomic velocities, we introduce the concepts of peak-forward and peak-away. Notably, we observe that negative amplitudes exclusively occur in the peak-forward transitions. This allows us to introduce a metric - the ratio of negative (positive) amplitude relative to the total peak-forward amplitude - as a quantitative evaluation of electromagnetically induced transparency (EIT) [Autler-Townes splitting (ATS)]. Furthermore, we propose an available observation to examine our theoretical simulations on the transition from EIT to ATS in a Doppler-broadened system. This approach can reflect the contributions of atoms with nonzero velocity, aside from the Rabi frequency of the control field, to the total EIT and ATS signals. It provides another theoretical viewpoint to distinguish the weights of EIT and ATS phenomena in Doppler-broadened atomic transition.